\(a,\Rightarrow2x^2-18x-2x^2=0\\ \Rightarrow-18x=0\Rightarrow x=0\\ b,\Rightarrow2x^2-5x-12+x^2-7x+10=3x^2-17x+20\\ \Rightarrow5x=22\Rightarrow x=\dfrac{22}{5}\)

a, Có : |2x-1| + |2x-5| = |2x-1| + |5-2x| >= |2x-1+5-2x| = 4

Dấu "=" xảy ra <=> (2x-1).(5-2x) = 0 <=> 1/2 < = x < = 5/2

Vậy 1/2 < = x < = 5/2

b, +, Nếu x < -3/4 => 3-x-3x-4 = -2x-1

=> ko tồn tại x

+, Nếu -3/4 < = x < = -1/2 => 3-x+3x+4 = -2x-1

=> x=-2 ( ko t/m )

+, Nếu -1/2 < x < = 3 => 3-x+3x+4=2x+1

=>ko tồn tại x

+, Nếu x > 3 => x-3+3x+4=2x+1

=> x=0 ( ko t/m )

Vậy ko tồn tại x t/m bài toán

Tham khảo xem có đúng ko nha !

\(D=\frac{2x+1}{x-3}=\frac{2x-6}{x-3}+\frac{7}{x-3}=2+\frac{7}{x-3}\in Z\Leftrightarrow x-3\inƯ\left(7\right)=\left\{-7;-1;1;7\right\}\)

\(\Leftrightarrow x\in\left\{-4;2;4;10\right\}\)

D= \(\frac{2x+1}{x-3}=2+\frac{7}{x-3}\)

để D dương thì x-3 là uocs của 7=(-1,1,-7,7)

xét từng TH: 

x-3=-1=> x=2

x-3=1=>x=4

x-3=-7=>x=-4

x-3=7=>x=10

các giá trị x là 2,4,-4,10

\(\left(x-2\right)\left(x^2+2x+4\right)-x\left(x-3\right)\left(x+3\right)=10\\ \Leftrightarrow x^3-8-x\left(x^2-9\right)=10\\ \Leftrightarrow x^3-8-x^3-9x=10\\ \Leftrightarrow-9x=18\\ \Leftrightarrow x=-2\)

x=2

(x−2)(x2+2x+4)−x(x−3)(x+3)=10⇔x3−8−x(x2−9)=10⇔x3−8−x3−9x=10⇔−9x=18⇔x=−2

Đặt t = 2x^2 +x pt trở thành

t^2 - 4t + 3=0

=>t^2 -t -3t +3 =0

=>t( t - 1) -3( t - 1)=0 

=>(t - 3)(t - 1 )=0 

*)Với t-3=0 <=> 2x^2 + x -3=0

=>2x^2 +3x -2x - 3 =0

=>x(2x + 3) - (2x + 3)=0

=>(x - 1)(2x + 3)=0 <=>x=1 hoặc x=-3/2

*)Với t-1=0 <=> 2x^2 + x -1=0

=>2x^2 - x + 2x -1=0

=>x(2x - 1) + (2x - 1) =0

=>(x + 1)(2x - 1)=0 <=> x=-1 hoặc x=1/2

b,|1-2x|+|5-2x|=4

==>|1-2x|+|5-2x|=|1-2x|+|2x-5|

==>|1-2x|+|2x-5| \(\geq\) |1-2x+2x-5|=|-4|=4

A \(\geq\) 4 khi \(\hept{\begin{cases}1-2x\\2x-5\end{cases}}\)\(\geq\) 0 ==>1/2\(\leq \) x \(\leq \) 5/2

a/ (x + 3)(x - 2) + 3x = 4(x + 3/4) 

     => x² + x - 6 + 3x = 4x + 3

     => x² = 9 => x = 3 hoặc x = -3 

              Vậy x = 3 , x = -3

b/ (x² - 5)(x + 2) + 5x = 2x² + 17

    => x³ + 2x² - 5x - 10 + 5x - 2x² - 17 = 0

    => x³ = 27 => x³ = 3³ => x = 3

                             Vậy x = 3

\(a,\Leftrightarrow9x^2=-36\Leftrightarrow x\in\varnothing\\ b,\Leftrightarrow3\left(x+4\right)-x\left(x+4\right)=0\\ \Leftrightarrow\left(3-x\right)\left(x+4\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=3\\x=-4\end{matrix}\right.\\ c,\Leftrightarrow2x^2-x-2x^2+3x+2=0\\ \Leftrightarrow2x=-2\Leftrightarrow x=-1\\ d,\Leftrightarrow\left(2x-3-2x\right)\left(2x-3+2x\right)=0\\ \Leftrightarrow-3\left(4x-3\right)=0\\ \Leftrightarrow x=\dfrac{3}{4}\\ e,\Leftrightarrow\dfrac{1}{3}x\left(x-9\right)=0\Leftrightarrow\left[{}\begin{matrix}x=0\\x=9\end{matrix}\right.\\ f,\Leftrightarrow x^2\left(x-1\right)-\left(x-1\right)=0\\ \Leftrightarrow\left(x^2-1\right)\left(x-1\right)=0\\ \Leftrightarrow\left(x-1\right)^2\left(x+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=1\\x=-1\end{matrix}\right.\)